The impact of braiding covariance and in-survey covariance on next-generation galaxy surveys

As galaxy surveys improve their precision thanks to lower levels of noise and the push toward small, non-linear scales, the need for accurate covariances beyond the classical Gaussian formula becomes more acute. Here I investigate the analytical implementation and impact of non-Gaussian covariance terms that I had previously derived for the galaxy angular power spectrum. Braiding covariance is such an interesting class of such terms and it gets contributions both from in-survey and super-survey modes, the latter proving difficult to calibrate through simulations. I present an approximation for braiding covariance which speeds up the process of numerical computation. I show that including braiding covariance is a necessary condition for including other non-Gaussian terms, namely the in-survey 2-, 3-, and 4-halo covariance. Indeed these terms yield incorrect covariance matrices with negative eigenvalues if considered on their own. I then move to quantify the impact on parameter constraints, with forecasts for a survey with Euclid-like galaxy density and angular scales. Compared with the Gaussian case, braiding and in-survey covariances significantly increase the error bars on cosmological parameters, in particular by 50% for the dark energy equation of state w. The error bars on the halo occupation distribution (HOD) parameters are also affected between 12% and 39%. Accounting for super-sample covariance (SSC) also increases parameter errors, by 90% for w and between 7% and 64% for HOD. In total, non-Gaussianity increases the error bar on w by 120% (between 15% and 80% for other cosmological parameters) and the error bars on HOD parameters between 17% and 85%. Accounting for the 1-halo trispectrum term on top of SSC, as has been done in some current analyses, is not sufficient for capturing the full non-Gaussian impact: braiding and the rest of in-survey covariance have to be accounted for. Finally, I discuss why the inclusion of non-Gaussianity generally eases up parameter degeneracies, making cosmological constraints more robust for astrophysical uncertainties. I released publicly the data and a Python notebook reproducing the results and plots of the article